Lesson Objectives

- Demonstrate an understanding of long division
- Demonstrate an understanding of division with decimals
- Learn how to convert a fraction into a decimal

## How to Convert a Fraction into a Decimal

In our last lesson, we learned how to divide decimals.
This knowledge will enable us to convert a fraction into a decimal. In order to convert a fraction into a decimal:

Example 1: Convert each fraction into a decimal

$$\frac{3}{4}$$ We will set up our long division with 3 (dividend) under the long division symbol and 4 (divisor) to the left of the long division symbol: We can see that 4 is larger than 3. This means we will need to place a decimal point after 3 and add a zero to the right in order to divide. Recall that:

3 = 3.0

Remember to bring the decimal point up into the answer: Now we can perform our division. We continue to add zeros until we have zero as a remainder or a repeating digit/series of digits: $$\frac{3}{4} = 0.75$$ Example 2: Convert each fraction into a decimal

$$\frac{9}{20}$$ We will set up our long division with 9 (dividend) under the long division symbol and 20 (divisor) to the left of the long division symbol: We can see that 20 is larger than 9. This means we will need to place a decimal point after 9 and add a zero to the right in order to divide. Recall that:

9 = 9.0

Remember to bring the decimal point up into the answer: Now we can perform our division. We continue to add zeros until we have zero as a remainder or a repeating digit/series of digits: $$\frac{9}{20} = 0.45$$ Example 3: Convert each fraction into a decimal

$$\frac{17}{30}$$ We will set up our long division with 17 (dividend) under the long division symbol and 30 (divisor) to the left of the long division symbol: We can see that 30 is larger than 17. This means we will need to place a decimal point after 17 and add a zero to the right in order to divide. Recall that:

17 = 17.0

Remember to bring the decimal point up into the answer: Now we can perform our division. We continue to add zeros until we have zero as a remainder or a repeating digit/series of digits: $$\frac{17}{30} = 0.5\overline{6}$$

- divide the numerator by the denominator
- Continue the division until the remainder is zero or a repeating digit/series of digits

Example 1: Convert each fraction into a decimal

$$\frac{3}{4}$$ We will set up our long division with 3 (dividend) under the long division symbol and 4 (divisor) to the left of the long division symbol: We can see that 4 is larger than 3. This means we will need to place a decimal point after 3 and add a zero to the right in order to divide. Recall that:

3 = 3.0

Remember to bring the decimal point up into the answer: Now we can perform our division. We continue to add zeros until we have zero as a remainder or a repeating digit/series of digits: $$\frac{3}{4} = 0.75$$ Example 2: Convert each fraction into a decimal

$$\frac{9}{20}$$ We will set up our long division with 9 (dividend) under the long division symbol and 20 (divisor) to the left of the long division symbol: We can see that 20 is larger than 9. This means we will need to place a decimal point after 9 and add a zero to the right in order to divide. Recall that:

9 = 9.0

Remember to bring the decimal point up into the answer: Now we can perform our division. We continue to add zeros until we have zero as a remainder or a repeating digit/series of digits: $$\frac{9}{20} = 0.45$$ Example 3: Convert each fraction into a decimal

$$\frac{17}{30}$$ We will set up our long division with 17 (dividend) under the long division symbol and 30 (divisor) to the left of the long division symbol: We can see that 30 is larger than 17. This means we will need to place a decimal point after 17 and add a zero to the right in order to divide. Recall that:

17 = 17.0

Remember to bring the decimal point up into the answer: Now we can perform our division. We continue to add zeros until we have zero as a remainder or a repeating digit/series of digits: $$\frac{17}{30} = 0.5\overline{6}$$

Ready for more?

Watch the Step by Step Video Lesson
Take the Practice Test